The present invention relates generally to an optimized non-tracking solar concentrator. More particularly, the present invention relates to a numerically optimized non-tracking solar concentrator utilizing symmetry-breaking surface and reflector structure.
It has been conventionally understood that solar concentrators placed in an east-west arrangement will receive light over a longer period of time and are generally more efficient than concentrators oriented in a north-south arrangement of the same size and shape. There are several reasons, however, why it can be beneficial to place solar concentrators in a north-south arrangement as opposed to an east-west arrangement.
Some advantages to a north-south orientation for concentrators arise, for example, from the collector plane being tilted in elevation, and thus a north-south arrangement allows a heat pipe to function properly since the heat pipe condenser, which is at the end of a receiver tube, must be located above the rest of the tube to enable gravitational forces to apply. In an east-west orientation, however, the tubes are horizontal and gravity does not assist the fluid return. Additionally, the connecting piping in a north-south arrangement is substantially horizontal, which is more efficient and less costly to construct than the substantially vertical arrangement required for an east-west oriented concentrator. Furthermore, north-south oriented collectors with CPC (compound parabolic concentrator) reflectors are somewhat self-cleaning with rainfall. As a result, glazing covers are often not necessary. With east-west oriented collectors, however, dirt and debris can accumulate, requiring that glazers be included. There has therefore been a desire to increase the performance characteristics of north-south collectors to take advantage of these beneficial qualities. Unfortunately, however, the nature of translationally symmetrical solar concentrators has resulted in north-south solar concentrators being very limited in performance for the reasons described herein below.
Using a conventional geometrical-optics approximation, the flux-transfer efficiency of passive optical systemsxe2x80x94such as lenses, reflectors, and combinations thereofxe2x80x94is limited by the principle of xc3xa9tendue conservation. For rotationally symmetric optical systems a further, more stringent limitation on flux-transfer efficiency is imposed by the fact that the skew invariant of each ray propagating through such systems is conserved. This performance limitation can, however, be overcome by breaking the symmetry of the optical system.
Translationally symmetric optical systems are subject to a performance limitation analogous to the limitation imposed by the skew invariant on rotationally symmetric systems. The performance limitations imposed on nonimaging optical systems by rotational and translational symmetry are a consequence of the well known Noether""s theorem, which relates symmetry to conservation laws.
A translationally symmetric nonimaging device is a nonimaging optical system for which all refractive and reflective optical surfaces have surface normal vectors that are everywhere perpendicular to a single Cartesian coordinate axis, referred to as the symmetry axis. In an optical ray incident on a translationally symmetric optical surface, the symmetry axis is assumed to be the z-axis of a Cartesian x,y,z-coordinate system. The incident ray is assumed to propagate through a medium of refractive index n0. The incident optical direction vector is defined as:
xe2x80x83{right arrow over (S)}0xe2x89xa1n0{right arrow over (Q)}0,xe2x80x83xe2x80x83(1)
where {right arrow over (Q)}0 is a unit vector pointing in the propagation direction of the incident ray. It is well known in the art that the component of the optical direction vector along the symmetry axis is conserved for all rays propagating through a translationally symmetric optical system. This follows from the vector formulation of the laws of reflection and refraction, in which the optical direction vector of a ray reflected or refracted by the optical surface is:
{right arrow over (S)}1={right arrow over (S)}0+xcex93{right arrow over (M)}1,xe2x80x83xe2x80x83(2)
where {right arrow over (M)}1 is the unit vector normal to the surface at the point of intersection of the incident ray with the surface. The formula for the quantity xcex93 is:
xcex93=2n0 cos(I)xe2x80x83xe2x80x83(3)
for reflection and:                     Γ        =                                            -                              n                0                                      ⁢            cos            ⁢                          xe2x80x83                        ⁢                          (              I              )                                +                                    n              1                        ⁢                                                                                                      (                                                                        n                          0                                                                          n                          1                                                                    )                                        2                                    ⁢                                                            cos                      2                                        ⁡                                          (                      I                      )                                                                      -                                                      (                                                                  n                        0                                                                    n                        1                                                              )                                    2                                +                1                                                                        (        4        )            
for refraction of the ray into a material of refractive index n1. In equations (3) and (4) for xcex93, the quantity I is the angle of incidence of the ray relative to the surface-normal vector. The unit vector {right arrow over (M)}1 in the above formulation is, by definition, perpendicular to the z axis, meaning that its z-component equals zero. From Eq. (2), it can be determined that the incident and reflected (or refracted) optical direction vectorsxe2x80x94{right arrow over (S)}0 and {right arrow over (S)}1xe2x80x94must have the same z-component. Since the z-axis is the symmetry axis, the component of the optical direction vector along the symmetry axis is invariant for any ray propagated through a translationally symmetric optical system. This invariant component of the optical direction vector is referred to as the translational skew invariant or the translational skewness. The fact that a translationally symmetric nonimaging system cannot alter the translational skew invariant, which is also referred to as skewness or the skew invariant, places a fundamental limitation on the flux-transfer efficiency achievable by such a system.
Translational skewness is a unitless quantity with an absolute value less than or equal to the refractive index. Translational skewness can be negative or positive depending on the ray direction relative to the z-axis. A ray that is perpendicular to the symmetry axis always has zero translational skewness. The only requirement for the translational skewness to be an invariant quantity is that the optical system be translationally symmetric. In particular, there is no requirement that either the radiation source or the target to which flux is to be transferred be symmetric.
Just as the rotational skewness of a ray is analogous to angular momentum measured relative to the symmetry axis of a rotationally symmetric optical system, translational skewness is analogous to the component of linear momentum along the symmetry axis of a translationally symmetric optical system. For example, in a small unit-velocity particle of mass equal to the index of refraction traveling along the ray path, the linear-momentum component of the particle along the translational symmetry axis is equal to the translational skewness of the ray. If the translational skewness of each individual ray entering an optical system is conserved, then the complete distribution of translational skewness for all emitted rays must also be conserved. As in the case of the rotational skewness, this places a much stronger condition on achievable performance than the conservation of phase-space volume, often referred to as xc3xa9tendue, which is a scalar quantity.
It has been held as conventional wisdom that the use of translationally symmetrical optical concentrators result in the most efficient energy collection. Using a translationally symmetrical, non-tracking concentrator, particularly in a north-south arrangement, is still severely limited in the amount of light that is collected during the day.
It is therefore an object of the invention to provide an improved non-tracking solar concentrator that can overcome the performance limitations associated with translational symmetry.
It is another object of the invention to provide an improved non-tracking solar concentrator that provides an increase in efficiency and concentration relative to an ideal translationally symmetric, non-tracking solar concentrator.
It is still another object of the invention to provide an improved non-tracking solar concentrator that increases the amount of time that light is collected during the day.
It is yet another object of the invention to provide an improved non-tracking solar concentrator that is arranged in a substantially north-south and inclined position.
In accordance with the above objects, a non-tracking solar concentrator includes a symmetry-breaking reflector. The symmetry-breaking reflector, which can exist in the form of ridges, indentations, facet arrangements, impressions, particle dispersions in a volume or other features, helps the concentrators overcome the performance limitations associated with translational symmetrical concentrators, resulting in an increase in performance relative to an ideal translationally symmetrical concentrator despite the conventional belief in the art that translationally non-symmetrical concentrators will provide inferior performance characteristics. Optimally positioned breaks in symmetry have substantial advantages such as, for example, assisting the collector in collecting light for a longer period of time during the day.